Final Report on COOMET Key Comparison of National Pressure Standards in the Range 100 Pa to 5 kpa of Gauge Pressure (COOMET.M.

Transcription

1 Verson 1 of Fnal Report on COOMET Key Comparson of Natonal Pressure Standards n the Range 100 Pa to 5 kpa of Gauge Pressure (COOMET.M.P-K14) H. Ahrendt 1, J. Könemann 1, W. Sabuga 1, Y. Kselev 2, O. Vtkovsky 2, D. Pražák 3, Z. Krajcek 3, K. Dapkevčenė 4, ABSTRACT Ths report descrbes a COOMET key comparson of pneumatc gauge pressure standards of four Natonal Metrology Insttutes, lsted n the chronologcal order of ther measurements, that was carred out n the perod from November 2008 to March 2010 n order to determne ther degree of equvalence n the range of 100 Pa to 5 kpa of gauge pressure. The plot laboratory was PTB. The reference pressure standards of the partcpants were of dfferent desgn. The transfer standard was a pston gauge model V1600 of the company Pressurements. The quantty under comparson was the effectve area of the transfer standard at dfferent pressure values reported together wth uncertanty contrbutons and the conclusve combned uncertanty of measurement. All partcpants results agree wth the key comparson reference values wthn the expanded uncertantes calculated wth a coverage factor 2, all but one results even wthn the standard uncertantes. For the partcpants results compared n pars, all of totally 48 pars show agreement wthn the expanded and 46 pars wthn the standard uncertantes. The results of the comparson demonstrate equvalence of the laboratory standards and support ther measurement capabltes stated n the KCDB of BIPM. 1 Physkalsch-Technsche Bundesanstalt (PTB), Braunschweg, Germany 2 D.I. Mendeleyev Insttute for Metrology (VNIIM), St. Petersburg, Russa 3 Czech Metrology Insttute (CMI), Brno, Czech Republc 4 Vlnus Metrology Centre (VMC), Vlnus, Lthuana

2 CONTENTS 1. INTRODUCTION PARTICIPANTS PTB pressure standards and measurement method VNIIM pressure standard and measurement method CMI pressure standard and measurement method VMC pressure standard and measurement method TRANSFER STANDARD ORGANIZATION AND CHRONOLOGY OF THE COMPARISON MEASUREMENT PROCEDURES RESULTS Stablty of the transfer standard Results of the Partcpants Reference value calculaton Degree of equvalence DISCUSSION CONCLUSIONS...20 REFERENCES...20 APPENDIX A. Relatve devatons of the partcpants results from the reference value ((A p, - A p,ref )/A p,ref ) wth the expanded uncertantes (k = 2) of these devatons at pressures 100 Pa to 5 kpa...21 APPENDIX B. Relatve dfferences between the partcpants results (d j ) and ther expanded uncertantes (U(d j )) (k = 2) at pressures 100 Pa to 5 kpa...24 APPENDIX C. Stablty of TS

3 1. INTRODUCTION At the COOMET TCM meetng held at KazInMetr, Astana, on 8 October 2008, t was decded to carry out a key comparson (KC) n the range of 5 kpa of pneumatc gauge pressure. Pont of am of ths comparson was to state the equvalence of the natonal pressure standards of the partcpatng natonal metrologcal laboratores n the 5 kpa range. Two partcpants n ths comparson, the Physkalsch-Technsche Bundesanstalt (PTB), Germany, and the Czech Metrology Insttute (CMI), Czech Republc, are also partcpants n the respectve KCs of EURAMET, EURAMET.M.P-K4.2010, beng n progress, and a CCM KC beng stll n preparaton. Ths wll allow a lnk of the current COOMET KC to the correspondng EURAMET and CCM KCs. PTB was agreed to be a plot laboratory n ths KC and provded a transfer standard (TS) for ths KC. The comparson was carred out n accordance wth ts Techncal Protocol whch specfed the procedures to be followed n the comparson and had been prepared n accordance wth the Gudelnes for CIPM Key Comparsons, 1 March PARTICIPANTS The laboratory standards (LS) used n ths comparson were of dfferent types, namely a dvng bell manometer, deadweght and force-controlled pston gauges, and a water column mcromanometer. Dfferent methods were appled by the partcpants to compare ther standards wth the TS. All uncertantes relatng to the partcpants standards and ther results n ths report are standard ones f not explctly ndcated as expanded. 2.1 PTB pressure standards and measurement method Two dfferent laboratory standards were used by PTB n ths KC. For the pressure values up to nomnally 4 kpa, the dvng bell known as TGM 5 wth the mass set dentfed by g01ma2 was compared to TS. Ths bell manometer was developed at the ASMW [1] and was transferred to PTB n 1990 actng there as a reference standard for small gauge and dfferental pressures up to 4 kpa. In order to cover ths pressure range t was equpped wth Fluornert nstead of nonane as a workng flud, and, moreover, the load mechansm was drectly attached to the bell. It was used n a comparson of European dfferental pressure standards from 3 Pa to 1 kpa [2]. The effectve area of the dvng bell s traceable to a prmary mercury manometer of PTB. Table 1 summarzes propertes of the dvng bell manometers and the related measurement condtons. 3

4 Table 1. PTB dvng bell manometer for pressures up to 4 kpa and measurement condtons Type of devce Dvng bell manometer Manufacturer ASMW, Germany Measurement range n Pa, mode (1 4000), gauge Materal of dvng bell or pston brass Workng lqud (for dvng bell manometer) Fluornert Pressure-transmttng gas Ar or ntrogen Zero-pressure effectve area (A 0 ) at reference temperature n m Relatve uncertanty of A 0 n Uncertanty of mass (m) peces or of mass measurement 125 mg m Lnear thermal expanson coeffcent of dvng bell manometer (α p ) n C Reference temperature (t 0 ) n C 20 Local gravty (g) n m/s Relatve uncertanty of g n Heght dfference between laboratory standard (LS) and TS (h, postve f LS s hgher than 0 TS) n mm Uncertanty of h n mm 5 For pressure values 4800 and 5000 Pa a gas-operated pressure balance TL1568 from Ruska company was used together wth the mass set p04ma. The propertes of ths pressure balance are presented n Table 2. 4

5 Table 2. PTB pressure balance for pressures of 4.8 and 5 kpa Type of devce Manufacturer Measurement range n kpa, mode Materal of dvng bell or pston Materal of cylnder (for pressure balance) Pressure-transmttng gas Zero-pressure effectve area (A 0 ) at reference temperature n m Relatve uncertanty of A 0 n Uncertanty of mass peces at p max, mg 3 Lnear thermal expanson coeffcent of dvng bell or pston (α p ) n C Lnear thermal expanson coeffcent of cylnder (for pressure balance, α c ) n C Reference temperature (t 0 ) n C 20 Local gravty (g) n m/s Relatve uncertanty of g n Heght dfference between laboratory standard (LS) and TS (h, postve f LS s hgher than TS) n mm TL1568 Ruska , gauge and absolute steel Tungsten carbde Dry gas/ntrogen Uncertanty of h n mm VNIIM pressure standard and measurement method The VNIIM pressure standard s a water column mcromanometer whch s a part of the natonal specal standard of unt of pressure GET (GOST «State system for ensurng the unformty of measurements. The State specal standard and All-Unon verfcaton schedule for means of measurements of the dfference of pressures up to Pa») havng desgnaton "MKШ". Physcally, t s a water-based compensated mcromanometer workng n a pressure range up to 5 kpa wth a traceablty of ts propertes to VNIIM standards. Wth the TS used n the KC and under the condtons of the experment, the maxmum pressure of the laboratory standard was lmted by 4.8 kpa. Hence, devatng from the Techncal Protocol, the hghest measured pressure was 4.8 kpa. TS was transported to VNIIM by the plot laboratory on 21 November 2008 and measured there between 24 and 26 November It was returned to PTB on 28 November The propertes of the VNIIM pressure standard and the measurement condtons are gven n Table 3. 5

6 Table 3. VNIIM water column mcromanometer and measurement condtons Type of devce Water column mcromanometer Manufacturer VNIIM, Russa Pressure (p) measurement range n Pa Relatve uncertanty of pressure for 100 Pa: for 5000 Pa: Workng lqud Dstlled water Densty of workng lqud (ρ l ) kg/m Relatve uncertanty of ρ l n Reference temperature of workng lqud (t 0 ) n C 20 Uncertanty of t 0 n C 0.1 Pressure-transmttng gas Ntrogen Local gravty (g) n m/s Relatve uncertanty of g n Heght dfference between laboratory standard (LS) and TS (h, postve f LS s hgher than 20 TS) n mm Uncertanty of h n mm CMI pressure standard and measurement method The CMI pressure standard used n ths comparson s a force-balanced pston gauge (FPG) manufactured by DH Instruments, USA, model FPG 8601, whose descrpton of the physcal prncple s descrbed n [3] and the commercal realsaton n [4]. The setup of the CMI FPG was modfed wth respect to the commercal one n such a way that a turbo-molecular pump was added to the pumpng system of the reference sde n order to reduce the resdual pressure on the reference sde and, therefore, ts uncertanty contrbuton. A thorough evaluaton of the CMI system s presented n [5]. The effectve area was evaluated both by a dmensonal measurement of the pstoncylnder geometry and by cross-floatng technques comparng t aganst the CMI PG 7601 pressure balance. These comparsons were performed wth the CMI standards durng the year An ntercomparson wth the Slovak natonal metrology nsttute (SMU) was performed n December 2002 from 2 to 15 kpa n both gauge and absolute pressure mode wth a Bell and Howell pressure balance as a transfer standard. Another ntercomparson wth the Fnnsh natonal metrology nsttute, (MIKES), was realzed n July 2003 from 1 Pa to 15 kpa n gauge pressure mode and from 6 Pa to 15 kpa n absolute pressure mode, the MIKES standard beng another FPG A thrd blateral comparson, EURAMET.M.P-S2, was carred out wth PTB that used an FRS5 force-compensated pressure balance manufactured by Furness Controls, UK. For the actual measurements an MKS Baratron dfferental pressure cell (DPC) was used as a zero pressure ndcator nstalled between the CMI FPG and the TS. Wth ths DPC CMI could automate the measurements usng software Compass of the FPG. The techncal detals of the CMI standard and the measurement condtons are gven n Table 4. 6

7 The transfer standard was transported to CMI by the plot laboratory on 11 May The measurements were performed n the perod from 12 to 13 May 2009, accordng to the Techncal Protocol. Afterwards, TS was brought back to PTB on 15 May Table 4. CMI force-balanced pston gauge and measurement condtons Type of devce FPG 8601 Manufacturer DH Instruments Measurement range n Pa , gauge and absolute Materal of dvng bell or pston tungsten-carbde Materal of cylnder (for pressure balance) tungsten-carbde Pressure-transmttng gas ntrogen Zero-pressure effectve area (A 0 ) at reference temperature n m Relatve uncertanty of A 0 n Uncertanty of mass (m) peces or of mass measurement 0.5 mg m Lnear thermal expanson coeffcent of dvng bell or pston (α p ) n C Lnear thermal expanson coeffcent of cylnder (for pressure balance, α c ) n C Reference temperature (t 0 ) n C 20 Local gravty (g) n m/s Relatve uncertanty of g n Heght dfference between laboratory standard (LS) and TS (h, postve f LS s hgher than 124 TS) n mm Uncertanty of h n mm 2/ VMC pressure standard and measurement method The VMC laboratory standard was a pston gauge Metran-505, Vozduch I, manufactured by Metran, Russa, seral number 094, made n The devce was calbrated at PTB (Germany) n August Thus, ts pressure value s traceable to the German natonal pressure standards. The pressure values realsed wth pstons M and B n combnaton wth weghts and the uncertantes of that pressure values were determned at PTB and reported n Calbraton certfcate Nr PTB Fnally, the effectve area A(p) of pston M assembly and pston B assembly were calculated at VMC. The techncal detals of the VMC standard and the measurement condtons are gven n Table 5. 7

8 Table 5. VMC pston gauge and measurement condtons Type of devce Metran-505, Vozduch I, seral Nr. 094 Manufacturer Metran Measurement range, mode 20 Pa to 25 kpa: gauge pressure 5 Pa to 25 kpa: dfferental pressure Materal of pstons up to 125 Pa - alumnum 160 Pa to 25 kpa - stanless steel Materal of cylnder (for pressure balance) stanless steel Pressure-transmttng gas Ar/ntrogen Zero-pressure effectve area (A 0 ) at reference temperature n m 2 3 pstons Relatve uncertanty of A 0 n Uncertanty of mass (m) peces or of mass measurement, mg 7.1 Lnear thermal expanson coeffcent of pston and cylnder (α p ) n C -1 (23±2) 10-6 Reference temperature (t 0 ) n C 20 Local gravty (g) n m/s Relatve uncertanty of g n Heght dfference between LS and TS (h, postve f LS s hgher than TS) n mm -6 Uncertanty of h n mm 5 TS and the laboratory standard were nterconnected va a DPC usng ntrogen as a pressure-transmttng medum. TS and the laboratory standard were loaded wth masses correspondng to the nomnal pressures as specfed n the Techncal Protocol and the resdual pressure dfferences between them were measured wth the DPC. Hence, the uncertanty of the DPC, whch accordng to the plot laboratory s Uncertanty of zero ndcator 0.02 Pa was added to the uncertanty of the VMC standard. TS was brought to VMC on 23 November 2009 and measured between 24 and 27 November, before t was returned to PTB on 27 November TRANSFER STANDARD The transfer standard was descrbed n detal n the techncal protocol. It was a pston gauge V1600/1D manufactured by Pressurements Ltd., Bedfordshre, England, n 1998 and dentfed by seral number The assembly conssted of a cylnder dentfed by seral number B 192, whch s engraved on the cylnder face, and three dfferent pstons all carryng number N 192 on the lower pston face and dentfed by markngs "1 mbar", "2 mbar" and "L". The nomnal effectve area of the assembly was A 0,nom = 4.91 cm 2. The cylnder s materal was stanless steel, whereas pston "1 mbar" was made of alumnum and pstons "2 mbar" and "L" were fabrcated agan from stanless steel. 8

9 Followng the manufacturer nformaton, the thermal expanson coeffcent of the assembly of cylnder and any of the pstons (ether of steel or of alumnum) was taken as (22 ± 2) 10-6 C -1 wth ts standard uncertanty based both on the manufacturer nformaton and the experence of the plot laboratory. Table 6. Masses and denstes of pstons Pston True mass n g Densty n kg/m 3 "1 mbar" ± ± 25 "2 mbar" ± ± 25 "L" ± ± 25 The weght carrer was marked wth "L" and made of alumnum. Table 7. Masses and denstes of the weght carrer Weght carrer True mass n g Densty n kg/m ± ± 25 Seven weghts were dentfed by markngs "1 mbar", "5 mbar", "10 mbar", "20_1 mbar", "20_2 mbar", and addtonally by seral number N192 on each pece. Table 8. Masses and denstes of the weghts Weght True mass n g Densty n kg/m 3 "1 mbar" ± ± 25 "2_1 mbar" ± ± 25 "2_2 mbar" ± ± 25 "5 mbar" ± ± 25 "10 mbar" ± ± 25 "20_1 mbar" ± ± 25 "20_2 mbar" ± ± 25 In combnaton wth the pston gauge, a zero pressure ndcator FC 014 was delvered to the partcpants, whch had been manufactured by Furness Controls and had seral number Ths ndcator had a scale nterval of 0.02 Pa and a maxmum dfferental pressure range of 100 Pa at a maxmum acceptable lne pressure of 100 kpa and a maxmum overload dfferental pressure of 100 kpa. 4. ORGANIZATION AND CHRONOLOGY OF THE COMPARISON The measurements were performed n the order and tmes gven n Table 9. 9

10 Table 9. Chronology of measurements Insttute Measurement start date Measurement end date PTB, ntal nvestgaton of TS 4 Nov Nov 2008 VNIIM 24 Nov Nov 2008 PTB, ntermedate check of TS 30 Mar Apr 2009 CMI 12 May May 2009 PTB, ntermedate check of TS 12 Nov Nov 2009 VMC 24 Nov Nov 2009 PTB, fnal check of TS 4 Mar Mar 2010 The plot laboratory performed three measurement cycles and one half-cycle measurement (November 2009) of TS. The measurement n March 2010 was taken as a PTB contrbuton to ths KC. 5. MEASUREMENT PROCEDURES The transfer standard had to be handled and the pston-cylnder assembly mounted n accordance wth the nstructons gven n the User s Manual Reference of the V1600 provded to the partcpants. TS was operated throughout all measurements by one member of the plot laboratory (Mrs. Ahrendt). The TS was recommended to be located close to the laboratory s reference standard to keep the pressure lne between the two nstruments as short as possble. The pston gauge V1600/ID of TS was equpped wth two cylnders. The cylnder dentfed by "B" was used n the comparson measurements. The reference level of TS was the upper face of cylnder B. The horzontalty of TS expected to be better than 0.1 mm/m was checked wth a sprt level placed on the upper face of cylnder B. The temperature of TS was measured wth a thermometer of the partcpant. It was attached to cylnder B of TS. The reference temperature of the comparson was 20 C. For measurements performed at a temperature devatng from 20 C, the effectve area of the TS was referred to 20 C usng the pston-cylnder thermal expanson coeffcent. The zero-pressure ndcator was swtched n the pressure lne between the gauge of TS and the laboratory standard to control equalty of the pressures generated by the two pressure standards and to avod pressure gradents along the lne. A bypass lne wth a valve was connectng both sdes of the zero ndcator to set ts zero readng. The workng gas of the assembly was ether dry ar or ntrogen. The pston gauge of TS dd not have any electroncs to be warmed up, but the zero-pressure ndcator had to be swtched on at least 5 mnute before the measurements. The pston had to be n a self-centred stable floatng poston. The tme between a pressure level change and the acquston of the data correspondng to the equlbrum of the laboratory standard and TS had to be not shorter than 3 mnutes. The measurements ncluded four cycles each wth nomnal pressures generated n the followng order (100, 200, 500, 1000, 2000, , 4000, 5000, 5000, 4000, 3000, 2000, 1000, 500, 200, 100) Pa. Thus, 64 measurements were performed n total. 10

11 Table 10. Load of TS to generate the nomnal pressures Nomnal pressure Loads (pstons, weght carrer, weghts) n Pa 100 Pston "1 mbar" 200 Pston "2 mbar" 500 Pston "L" + weght carrer "L"+ "1 mbar" 1000 Pston "L" + weght carrer "L" + "1 mbar" + "5 mbar" 2000 Pston "L" + weght carrer "L" + "1 mbar" + "5 mbar" + "10 mbar" 3000 Pston "L" + weght carrer "L" + "1 mbar" + "5 mbar" + "20_1 mbar" 4000 Pston "L" + weght carrer "L" + "1 mbar" + "5 mbar" + "10 mbar" + "20_1 mbar" 5000 Pston "L" + weght carrer "L" + "1 mbar" + "5 mbar" + "20_1 mbar" +"20_2 mbar" Due to measurement set-up of the actual comparson, VNIIM was only able to measure a nomnal pressure value of 4800 Pa as the hghest achevable, see secton 2.2. The correspondng combnaton of mass peces for ths pont was the followng: Table 11. Load of TS to generate the nomnal pressure of 4800 Pa Nomnal pressure n Pa 4800 Loads (pstons, weght carrer, weghts) Pston "L" + weght carrer "L" + "2_1 mbar" +"2_2 mbar" + "20_1 mbar" +"20_2 mbar" Comparablty of the results obtaned at ths pressure wth the results of other partcpants obtaned at 5 kpa was determned by measurements of the plot laboratory performed at both nomnal pressures, 4.8 and 5 kpa. No addtonal/dfferent loads were appled to the pstons of TS. The equlbrum between TS and the laboratory standard, whch was controlled wth the help of the zero-pressure ndcator, was acheved by adjustng the pressure n the laboratory standard. In the case of VMC usng a smlar devce to TS as a laboratory standard, the zero ndcator readng was used as a drect measure of the pressure dfference between TS and LS. The effectve area of the TS determned for a partcular measurement (A p ) referred to 20 C was calculated wth the equaton A p = g m ( 1 ρa / ρ ) p [1 + ( α + β )( t 20 C) ], (1) where m are true masses of the pston, the weght carrer and the mass peces placed on the weght carrer of TS; ρ are denstes of the parts wth masses m ; 11

12 ρ a s ar densty; g s local gravty acceleraton; p s pressure generated by the laboratory standard at the TS reference level; (α+β) s thermal expanson coeffcent of the pston-cylnder; t s temperature of TS. The values of p and ρ a were calculated and t was measured by the partcpatng laboratory. The condtons of the measurements are gven n Annexes A1-A4. 6. RESULTS 6.1 Stablty of the transfer standard Pror to the comparson, the long-term stablty of TS has been evaluated on the bass of calbraton results obtaned n 1999, 2001 and 2007 (Fgs. 1 and 2). green 2001 blue 1999 magenta Pa Gauge pressure n Pa Fgure 1. Devatons from reference pressure, pstons "1 mbar" and "2 mbar" 12

13 green 2001 purple 1999 magenta Pa Gauge pressure n Pa Fgure 2. Devatons from reference pressure, pston "L" As a result, no systematc changes could be seen at pressures up to 200 Pa. At the maxmum pressure of 5 kpa, the dfferences dd not exceed 1 Pa. Durng the comparson, the TS stablty was measured by the plot laboratory at the begnnng, n the mddle, and at the end of the comparson. The results for the one year perod of the actual KC are presented n Fgs. 3 and 4. Durng the tme of the KC, the plot laboratory performed four measurements n March 2010, November 2009, March 2009 and November 2008, see table 8, although the measurements of November 2009 ncluded only one measurement at each pressure. Fgure 3. Stablty of the transfer standard. Mean effectve areas and ther standard uncertantes for pstons "1 mbar" and "2 mbar" measured by PTB n 2008, 2009 and

14 Fgure 4. Stablty of the transfer standard. Mean effectve areas and ther standard uncertantes for pston L measured by PTB n 2008, 2009 and 2010 From an analyss of these results, see Appendx C, t could be concluded that the TS dd not underlay any systematc tme drft durng ths KC. Therefore, no tme dependent correcton was appled to the partcpants' results, and the nstablty of TS, u nstab (A p ), was expressed by the standard devaton of the mean values of the effectve area measured by the plot lab for each nomnal pressure, A p,plot, mean : N Ap, plot, mean = Ap, plot, N, (2) = 1 N 2 ( A ) ( A A ) ( N ) u nstab p = p, plot, p, plot, mean 1, (3) = 1 where N s number of plot laboratory measurements over the tme of the comparson, N = 4. The uncertanty of the TS determned n ths way s presented n Table 12. Table 12. Uncertanty contrbuton due to nstablty of TS, u nstab (A p ) Nomnal pressure n Pa u nstab (A p ) / mm 2 u nstab (A p )/A p Fgures 5 and 6 show relatve devatons of the effectve areas measured by the plot four tmes from ther mean values. It s obvous that no systematc tme drft occurred. Hence, the partcpants values of the effectve areas dd not have to be corrected for the comparson

15 Fgure 5. Instablty of TS: Relatve devatons of the sngle effectve areas from the mean ones of pstons "1 mbar" and "2 mbar" measured by the plot laboratory together wth the relatve standard devatons of the mean values (uncertanty bars) extracted from Table 12 Fgure 6. Instablty of TS: Relatve devatons of the sngle effectve areas from the mean ones of pston "L" measured by the plot laboratory together wth the relatve standard devatons of the mean values (uncertanty bars) extracted from Table Results of the Partcpants The mean effectve areas, the standard devatons of the effectve areas at each pressure and the combned relatve standard uncertantes of the effectve areas reported by the partcpants are presented n Table 13. The graphcal vsualzaton of the summary of all measurement cycles and partcpants s gven n Fgures 7 and 8. 15

16 Table 13. Mean effectve areas (<A p >), ther relatve standard devatons (s(a p )/A p ), relatve standard uncertantes of pressures (u(p)/p), standard uncertanty of the temperature of TS (u(t)) and combned standard uncertantes of the mean effectve areas (u(a p )/A p ) Nomnal pressure n Pa <A p> s(a p)/a p u(p)/p u(t) / mm 2 / C PTB VNIIM CMI VMC u(a p)/a p <A p> s(a p)/a p u(p)/p u(t) / mm 2 / C u(a p)/a p <A p> s(a p)/a p u(p)/p u(t) / mm 2 / C u(a p)/a p <A p> s(a p)/a p u(p)/p u(t) / mm 2 / C u(a p)/a p 16

17 A p / mm PTB 2010 CMI VNIIM VMC p / Pa Fgure 7. Mean effectve areas and ther uncertantes of TS wth pstons "1 mbar" and "2 mbar" determned by the partcpants A p / mm PTB 2010 CMI VNIIM VMC p / Pa Fgure 8. Mean effectve areas and ther uncertantes of TS wth pston "L" determned by the partcpants 17

18 6.3 Reference value calculaton The key comparson reference value (KCRV), A p,ref, was calculated at each pressure pont of the KC as a weghted mean, see eq. (4), where N s the number of the ndependent partcpants, PTB, CMI and VNIIM, N = 3, A p, and u(a p, )/A p, are the mean effectve area and ts uncertanty, respectvely, of partcpant at pressure p. Ths method s recommended n [6] and has been used for evaluaton of numerous KCs. The uncertanty of A p,ref, u(a p,ref ), was calculated by equaton (5). The weghted mean method s applcable only when the results of the partcpants succeed the consstency check based on the ch-squared test. Results are consdered as consstent f the observed ch-squared value χ 2 obs calculated by (6) s smaller than the value of the ch-square dstrbuton calculated for degree of freedom ν = N 1 at probablty Pr = 0.05, χ 2 (ν, Pr). A p,ref = N u A 2 = 1 p, N 1 p, ( ) 2 A u ( A ) 1 (,ref ) = N Ap 2 1 u ( Ap, ) N ( ) 2 Ap, Ap,ref obs = 2 u ( A ) = 1 p, 0.5 = u (5) = 1 p, 2 χ (6) Note, that although four NMIs partcpated n ths KC, VMC was excluded from the evaluaton of KCRV snce t s traceable to PTB (calbraton certfcate Nr PTB 2009, see secton 2.4) and, hence, s statstcally not ndependent. Takng nto account the nstablty of TS as defned by equaton (3), the combned standard uncertanty of KCRV, u*(a p,ref ), s defned as u*(a p,ref ) = [u 2 (A p,ref ) + u 2 nstab(a p )] 0.5. (7) Results of the KCRV evaluaton are summarsed n Table 14. Table 14. Key comparson reference values (A p,ref ), ther relatve standard uncertantes (u(a p,ref )/A p,ref ) and uncertantes combned wth the TS nstablty (u*(a p,ref )/A p,ref ) as well as parameters of the ch-squared test χ 2 obs and χ 2 (ν, 0.05) Nomnal pressure n Pa A p,ref / u(a p,ref ) / u*(a p,ref ) / mm 2 A p,ref A p,ref χ 2 obs χ 2 (ν, 0.05), ν = N (4) 18

19 1) Ths value of A p,ref was obtaned by combnng the PTB and CMI results obtaned at 5 kpa wth the result of VNIIM obtaned at 4.8 kpa. Such a combnaton s justfed by the measurements of the plot laboratory performed at pressures of 4.8 and 5 kpa whch showed no dfference n the effectve area. The consstency check supports the choce of the KCRV calculaton as a weghted mean. 6.4 Degree of equvalence The degrees of equvalence of the partcpants n relaton to KCRV consdered at each pressure are expressed n terms of relatve devatons of the partcpants' results from KCRV ( A p, / A p,ref ) and relatve expanded uncertantes of these devatons (U( A p, ) / A p,ref ), the latter beng calculated as: ( Ap, ) Ap,ref = 2 [ u ( Ap, ) u ( Ap,ref ) unstab ( Ap )] Ap, ref U +. (8) Numercal data for the devatons and the uncertantes at all pressures are lsted n Table 15, a graphcal presentaton s gven n Appendx A. Table 15. Relatve devatons of the partcpants results from the reference values ( A p /A p ) and ther expanded uncertantes (U( A p /A p )) Nomnal pressure (Pa) Ap /Ap PTB VNIIM CMI VMC U( Ap/Ap) Ap /Ap U( Ap/Ap) Ap /Ap U( Ap/Ap) Ap /Ap U( Ap/Ap) The degrees of equvalence between the laboratores are expressed by relatve dfferences between them (d j ) and relatve expanded uncertantes of these dfferences (U(d j )) calculated as: d ( Ap, Ap, j ) Ap, ref ( d ) [ ( ) ( ) ( )] 1 j 2 u Ap, + u Ap, j unstab Ap Ap, ref j =, (9) U = +, (10) whch are presented n the tables n Appendx B. 19

20 7. DISCUSSION From Table 13, the approprate performance of TS can be deduced. At the hghest pressure of 5 kpa, the typcal relatve standard devatons of A p of the partcpants range from 5 ppm to 80 ppm. A comparson of s(a p ) wth u(a p ) ndcates that for most NMIs n ths KC a major contrbuton to the uncertanty of A p was from the uncertanty of the laboratory standards. Comparson of typcal s(a p )/A p values from laboratory to laboratory clearly show dfferent performance of pressure measurements of the partcpatng NMIs. Among the laboratores, all values of the reported A p agree wthn ther expanded uncertantes (k = 2). All NMIs agree wth the reference value of KC wthn ther expanded uncertantes (k = 2), (Table 15 and Appendx A). The most results agree wth the reference value of the KC even wthn ther standard uncertantes (k = 1) except for PTB at 5 kpa. A comparson n pars demonstrates that the results of all partcpants agree wth each other wthn ther expanded uncertantes (k = 2) at all pressures (Appendx B). Wthn 48 compared pars of results, n no case there s a dsagreement on the level of the expanded uncertantes (k = 2). Only n two cases there are dfferences between the laboratores whch are bgger than the standard uncertantes of these dfferences. 8. CONCLUSIONS The transfer standard was stable wthn Pa p n terms of pressure n the perod of the KC. For all laboratores all the results are equvalent wth the key comparson reference values wthn the expanded uncertantes (k = 2), all but one results even wthn the standard uncertantes. For the NMIs results compared n pars, all of totally 48 pars show agreement wthn the expanded (k = 2) and 46 pars wthn the standard uncertantes. Wth the results of ths comparson PTB, VNIIM, CMI and VMC have supported ther measurement capabltes stated n the KCDB of BIPM. REFERENCES [1] Pppg E., Uhthoff E., Tauchglocken-Manometer als Gruppen-Prmärnormal des ASMW zur Darstellung der Druckskala m Überdruckberech bs 1600 Pa, Fengerätetechnk, 24 (1975) 20 [2] Perkn M. et al., Comparson of European dfferental pressure standards n the range 3 Pa to 1000 Pa, Metrologa, 36 (1999) 1 [3] Oowa A., Novel Nonrotatonal Pston Gauge wth Weght Balance Mechansm for the Measurement of Small Dfferental Pressures, Metrologa, 30 (1994) 607 [4] Delajoud P., Grard M., Pston gauge wth electronc balance for calbratons of very low pressures, Vakuum n Forschung und Praxs, 15 (2003) 24 [5] Tesar J., Repa P., Prazak D., Krajcek Z., Peksa L., The new method of traceablty of a force balanced pston gauge used as prmary vacuum standard, Vacuum, 76 ( 2004) 491 [6] Cox M.G., The evaluaton of key comparson data, Metrologa, 39 (2002)

21 APPENDIX A. Relatve devatons of the partcpants results from the reference value ((Ap, - Ap,ref)/Ap,ref) wth the expanded uncertantes (k = 2) of these devatons at pressures 100 Pa to 5 kpa 100 Pa: 200 Pa: 21

22 500 Pa: 1000 Pa: 2000 Pa: 22

23 3000 Pa: 4000 Pa: 5000 Pa: 23

24 APPENDIX B. Relatve dfferences between the partcpants results () and ther expanded uncertantes () (k = 2) at pressures 100 Pa to 5 kpa j p = 100 Pa CMI VNIIM PTB VMC CMI VNIIM PTB VMC j p = 200 Pa CMI VNIIM PTB VMC CMI VNIIM PTB VMC j p = 500 Pa CMI VNIIM PTB VMC CMI VNIIM PTB VMC j p = 1 kpa CMI VNIIM PTB VMC CMI VNIIM PTB VMC

25 j p = 2 kpa CMI VNIIM PTB VMC CMI VNIIM PTB VMC j p =3 kpa CMI VNIIM PTB VMC CMI VNIIM PTB VMC j p = 4 kpa CMI VNIIM PTB VMC CMI VNIIM PTB VMC j p = 5 kpa CMI VNIIM PTB VMC CMI VNIIM PTB VMC

26 APPENDIX C. Stablty of TS The followng dscusson focuses by chance on the nomnal pressure pont of 3000 Pa as a typcal data pont, compare to the whole dataset of TS measurements at the plot laboratory n Fg. 12. It could be shown that a lnear ft wthout slope contanng all measurements wthout weghng procedure yelded a satsfyng result ndcatng the stablty of TS. Performng a weghted lnear ft y = ax + b the followng values for a and b were obtaned b = ± mm 2 and a = (2.36 ± 3.57) 10-5 mm 2 /day, see Fgure C1. Fgure C1. Weghted lnear ft of the mean effectve areas wth correspondng combned uncertantes at p = 3000 Pa measured n March 2010 (0 days), March 2009 and November 2008, assumng a tme drft. Due to the uncertantes of the ft, a constant zero slope was deduced as a consequence,.e. t was assumed that bascally the TS had no systematc drft durng the tme of the comparson. Fgure C2. Weghted lnear ft of the mean effectve areas wth correspondng combned uncertantes at p = 3000 Pa measured n March 2010 (0 days), March 2009 and November 2008, assumng no tme drft. On the other hand, the TS s assocated wth a tme-constant uncertanty to be evaluated. Performng a weghted lnear ft y = ax + b assumng a = 0 we obtaned 26

27 then b = ± mm 2 (Fgure C2). Ths analyss was compared wth a nonweghted lnear ft wth zero-slope, see Fgure C3. Fgure C3. Non-weghted lnear ft of the mean effectve areas wth correspondng combned uncertantes at p = 3000 Pa measured n March 2010 (0 days), March 2009 and November 2008, assumng no tme drft. We ganed b = ± mm 2. Fnally, we analysed all data ponts avalable,.e. we consdered the sngle pressure-value measurements n November 2009 for a non-weghted lnear ft wth zero-slope, see Fgure C4. Fgure C4. Non-weghted lnear ft of the mean effectve areas wth correspondng combned uncertantes at p = 3000 Pa measured n March 2010 (0 days), November 2009, March 2009 and November 2008, assumng no tme drft. The result s then b = ± mm 2. Hence, we realzed that the dfferent analyses wth zero-slope bascally yelded smlar results. Consequently, we performed non-weghted lnear fts wth the complete data set to estmate the uncertanty of TS due to ts nstablty. 27